Anytime Day Return from Chester to any station on the Liverpool Loop is 7.80 on Merseyrail via Birkenhead, and 7.50 on TfW via Runcorn (to S Parkway/Lime St only).
With a 16-25 railcard these reduce to 5.15 on ME and 4.95 on TfW.
There are 4tph on the Merseyrail route, calling at all Loop stations, but only 1tph on TfW, calling at South Parkway and Lime St only.
These tickets cannot be interchanged, though there is a higher fare (12.60 or 8.30 with a railcard) which allows you to travel via either route (and via Warrington).
The higher fare also applies, for instance, if you go Chester-Liverpool S Parkway and change there on to Merseyrail to reach Moorfields.
The
cheapest route is Chester-Lime St via Runcorn, then walk to Moorfields!
The same fares are charged from Bache on Merseyrail, but Bache-Chester-Runcorn-Lime St on TfW will trigger the higher fare.
Railcards don't work with season tickets, so there is only the full fare.
The 7-day season ticket is 35.50 on ME and 29.30 on TfW.
Merseyrail also has a weekly Railpass on a Walrus card for 33.50.
There are deeper discounts for monthly/annual periods.
On a 5-day travel basis, the weekly season tickets are more expensive than the day tickets with railcard discount , but you have to buy the railcard up front (£30 for 1 year, £70 for 3 years).
Season tickets also avoid the booking office queues (Chester and Bache have ticket machines - Bache is unstaffed and has a tiny car park).
https://www.merseyrail.org/tickets-passes/season-tickets/railpass.aspx
Hope this helps!
PS Sorry, the 16-25 railcard has a minimum fare of £12 Mon-Fri except during July and August (so the date I checked showed the discount!).
So disregard the railcard fares I quoted above.